Efficient Yield Estimation of Multiband Patch Antennas by Polynomial Chaos-Based Kriging

Yield estimation of antenna systems is important to check their robustness with respect to the uncertain sources. Since direct Monte Carlo sampling of accurate physics-based models can be computationally intensive, this work proposes the use of the polynomial chaos–Kriging (PC-Kriging) metamodeling method for fast yield estimation of multiband patch antennas. PC-Kriging integrates the polynomial chaos expansion (PCE) as the trend function of Kriging metamodel since the PCE is good at capturing the function tendency and Kriging is good at matching the observations at training points. The PC-Kriging method is demonstrated on two analytical cases and two multiband patch antenna cases and is compared with the PCE and Kriging metamodeling methods. In the analytical cases, PC-Kriging reduces the computational cost by over 40% compared with PCE and over 94% compared with Kriging. In the antenna cases, PC-Kriging reduces the computational cost by over 60% compared with Kriging and over 90% compared with PCE. In all cases, the savings are obtained without compromising the accuracy

Phase Transitions of the Typical Algorithmic Complexity of the Random Satisfiability Problem Studied with Linear Programming

Here we study the NP-complete $K$-SAT problem. Although the worst-case complexity of NP-complete problems is conjectured to be exponential, there exist parametrized random ensembles of problems where solutions can typically be found in polynomial time for suitable ranges of the parameter. In fact, random $K$-SAT, with $\alpha=M/N$ as control parameter, can be solved quickly for small enough values of $\alpha$. It shows a phase transition between a satisfiable phase and an unsatisfiable phase. For branch and bound algorithms, which operate in the space of feasible Boolean configurations, the empirically hardest problems are located only close to this phase transition. Here we study $K$-SAT ($K=3,4$) and the related optimization problem MAX-SAT by a linear programming approach, which is widely used for practical problems and allows for polynomial run time. In contrast to branch and bound it operates outside the space of feasible configurations. On the other hand, finding a solution within polynomial time is not guaranteed. We investigated several variants like including artificial objective functions, so called cutting-plane approaches, and a mapping to the NP-complete vertex-cover problem. We observed several easy-hard transitions, from where the problems are typically solvable (in polynomial time) using the given algorithms, respectively, to where they are not solvable in polynomial time. For the related vertex-cover problem on random graphs these easy-hard transitions can be identified with structural properties of the graphs, like percolation transitions. For the present random $K$-SAT problem we have investigated numerous structural properties also exhibiting clear transitions, but they appear not be correlated to the here observed easy-hard transitions. This renders the behaviour of random $K$-SAT more complex than, e.g., the vertex-cover problem.Comment: 11 pages, 5 figure

Development of Methods for Uncertainty Quantification in CFD Applied to Wind Turbine Wake Prediction

The CFD 2030 vision aims to improve computer simulations of fluid dynamics in fields like aerospace and energy. They focus on managing uncertainties in these simulations. This study presents two methods:1. Intrusive Polynomial Chaos (IPC) Stochastic Solver: This method employs Polynomial Chaos expansion to tackle uncertainties linked to fluid flow simulations. It characterizes parametric uncertainties, studying their nonlinear effects. The solver is tested on various scenarios, showing its promise for reliable Uncertainty Quantification (UQ) analysis in CFD without being overly intrusive or costly.2. Surrogate Based Uncertainty Quantification (SBUQ) using Deep Learning: A novel approach involves constructing a surrogate model using a neural network, capable of predicting wind flow within a wind farm based on single wind turbine data. This model is used to assess uncertainty in wind farm predictions, accounting for parameter and model form uncertainties.These techniques were tested on different scenarios and demonstrated their capability to analyze complex CFD simulations under various uncertainties. They contribute to the potential of enhancing accuracy and efficiency in UQ analysis. The IPC-based stochastic solver integrates efficiently with existing code, while the SBUQ approach utilizes data from individual wind turbine simulations to predict flow patterns in wind farms.Both methods enhance the accuracy of fluid simulations under different uncertainties. This research contributes to more dependable simulations for aerospace, energy, and environmental engineering applications

Efficient statistical simulation of microwave devices via stochastic testing-based circuit equivalents of nonlinear components

This paper delivers a considerable improvement in the framework of the statistical simulation of highly nonlinear devices via polynomial chaos-based circuit equivalents. Specifically, a far more efficient and "black-box" approach is proposed that reduces the model complexity for nonlinear components. Based on recent literature, the "stochastic testing" method is used in place of a Galerkin approach to find the pertinent circuit equivalents. The technique is demonstrated via the statistical analysis of a low-noise power amplifier and its features in terms of accuracy and efficiency are highlighted

Stochastic Testing Method for Transistor-Level Uncertainty Quantification Based on Generalized Polynomial Chaos

Uncertainties have become a major concern in integrated circuit design. In order to avoid the huge number of repeated simulations in conventional Monte Carlo flows, this paper presents an intrusive spectral simulator for statistical circuit analysis. Our simulator employs the recently developed generalized polynomial chaos expansion to perform uncertainty quantification of nonlinear transistor circuits with both Gaussian and non-Gaussian random parameters. We modify the nonintrusive stochastic collocation (SC) method and develop an intrusive variant called stochastic testing (ST) method. Compared with the popular intrusive stochastic Galerkin (SG) method, the coupled deterministic equations resulting from our proposed ST method can be solved in a decoupled manner at each time point. At the same time, ST requires fewer samples and allows more flexible time step size controls than directly using a nonintrusive SC solver. These two properties make ST more efficient than SG and than existing SC methods, and more suitable for time-domain circuit simulation. Simulation results of several digital, analog and RF circuits are reported. Since our algorithm is based on generic mathematical models, the proposed ST algorithm can be applied to many other engineering problems